Firstly, I would like to understand if you have a proper relieving from your previous employer. If yes, you can always ask them to give you a salary certificate, which suffices your need. Even if you do not have a proper relieving, you can try checking with them.
Otherwise, you can even tell your future employer as you couldn't submit the payslip as they do not have payslips as such and I am sure, they would consider.
Also, you missed mentioning your tenure with the previous employer. If your have served them for a very small period of time, most of the companies do not consider your past employment.
Even further queries? you can reach me at the undersigned.
Thanks & Regards,
Dikshit T G S,
Human Resources Professional,
8th February 2013 From India, Hyderabad